The invention relates to a method and a device for coherently demodulating a frequency-modulated signal with a continuous phase.
A large number of digital modulation types are known, which are based on Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK) or Phase Shift Keying (PSK) methods as well as mixed forms of them. For frequency economy reasons, so-called CPM (Continuous Phase Modulation) modulation types with a continuous phase are frequently used in digital communications systems. FSK with a continuous phase is referred to as CPFSK (Continuous Phase FSK). One example of this is Gaussian Minimum Shift Keying (GMSK), which is used in the pan-European GSM (Global System for Mobile Communictions) mobile radio standard.
Coherent or incoherent methods may be used for demodulating the CPFSK signal. Incoherent demodulation may be carried out either by using an analog FM demodulator or digitally by using a differential demodulator. One disadvantage is that relatively high losses in the region of 3 dB occur with incoherent demodulation. Furthermore, drops in power occur, since the Inter Symbol Interference (ISI) cannot be taken into account.
CPFSK modulation, which is primarily non-linear, can be described approximately as linear modulation. The linear approximation on which this characteristic is based is described in the article xe2x80x9cExact and Approximate Construction of Digital Phase Modulations by Superposition of Amplitude Modulated Pulses (AMP)xe2x80x9d by Pierre A. Laurent, IEEE Trans. Commun., Volume COM-34 (1986), pages 150-160. This characteristic of CPFSK-modulated signals provides the capability for coherent demodulation.
The book xe2x80x9cNachrichtenxc3xcbertragungxe2x80x9d [Information transmission] by K. D. Kammeyer, B. G. Teubner Verlag, Stuttgart 1996, Section 12.1.5, pages 422 and 423, which represents the closest prior art, describes a coherent demodulator for CPFSK signals with a modulation index xcex7, which is equal to 0.5 or to a multiple of 0.5. The in-phase and quadrature branches of the received signal are sampled alternately (because of the 90xc2x0 phase offset between these branches), and the sample values obtained are compared with the corresponding complex-value representations of the CPFSK substitute symbols (on which the linear approximation is based) for the input data symbols used at the transmitter. Among the possible input data symbols, the input data symbol that is actually transmitted is defined as the one whose complex-value substitute symbol comes closest to the two measured sample values (real and imaginary part).
This coherent demodulation method for CPFSK signals can be generalized to rational modulation indices xcex7=M/N (where M and N are integers). With rational modulation indices, there are always a finite number of substitute symbol states, so that the demodulation can still be carried out just by comparing the sample values with the finite modulation alphabet of substitute symbols.
There is no longer any finite modulation alphabet of substitute symbols for non-rational modulation indices xcex7. The result of this is that the conventional method for coherent CPFSK demodulation can no longer be used in these situations.
It is accordingly an object of the invention to provide a method and a device for demodulating a CPFSK-modulated received signal, which overcome the above-mentioned disadvantages of the prior art methods and apparatus of this general type.
In particular, it is an object of the invention to provide a method and a device for demodulating CPFSK received signals, which enables good reception and enables the CPFSK received signal to be demodulated even when the modulation indices are not rational.
With the foregoing and other objects in view there is provided, in accordance with the invention, a method for demodulating a CPFSK-modulated signal. The method includes steps of: obtaining an estimate of an nxe2x88x921-th substitute symbol, which occurs in a linear approximation of the CPFSK modulated signal, as a function of a previously determined nxe2x88x921-th input data symbol; and determining an n-th input data symbol on which the CPFSK modulated signal is based by using the estimate of the nxe2x88x921-th substitute symbol occurring in the linear approximation of the CPFSK modulated signal.
In accordance with an added feature of the invention, the step of obtaining the estimate of the nxe2x88x921-th substitute symbol includes using an equation xc3xa2nxe2x88x921=xc3xa2nxe2x88x922exp{jxcfx80xcex7{circumflex over (d)}nxe2x88x921}, where xc3xa2hd nxe2x88x921 is the estimate for the nxe2x88x921-th substitute symbol, xc3xa2nxe2x88x922 is an estimate for an nxe2x88x922-th substitute symbol, {circumflex over (d)}nxe2x88x921 is the nxe2x88x921-th input data symbol that has been determined, and xcex7 denotes a modulation index.
In accordance with an additional feature of the invention, the step of determining the n-th input data symbol includes determining the n-th input data symbol dn based on a phase angle of a currently obtained n-th complex-value sample symbol yn relative to a phase angle of the estimate of nxe2x88x921-th substitute symbol xc3xa2nxe2x88x921 that has been estimated for an nxe2x88x921-th time step.
In accordance with another feature of the invention, the step of determining the n-th input data symbol dn includes obtaining a determined value of the n-th input data symbol dn using an equation:             d      ^        n    =      {                                        1                                                              arg                ⁡                                  (                                      y                    n                                    )                                             greater than                               arg                ⁡                                  (                                                            a                      ^                                                              n                      -                      1                                                        )                                                                                                        -              1                                                                          arg                ⁡                                  (                                      y                    n                                    )                                             less than                               arg                ⁡                                  (                                                            a                      ^                                                              n                      -                      1                                                        )                                                                        ;      
where {circumflex over (d)}n is the determined value of the n-th input data symbol dn.
In accordance with a further feature of the invention, the method includes using an equalizer, and in an even more preferred embodiment, the method includes using a Viterbi equalizer for performing the step of determining the n-th input data symbol dn.
In accordance with a further added feature of the invention, the step of obtaining the equalization includes basing the equalization on a trellis state diagram, in which an i-th channel state relating to a time step n is described by an L-tuple Zni=(znLxe2x88x921,(i), . . . , zn1,(i), zn0,(i)). In the equation, znLxe2x88x921,(i), . . . , zn1,(i), zn0,(i) can each assume possible values of input data symbols dn, and L denotes a channel memory.
With the foregoing and other objects in view there is also provided, in accordance with the invention, a device for demodulating a CPFSK-modulated signal. The device includes: an input data symbol decision device for determining an n-th input data symbol on which the CPFSK-modulated signal is based; and a substitute symbol estimation device for estimating an nxe2x88x921-th substitute symbol occurring in a linear approximation of the CPFSK-modulated signal as a function of a previously determined nxe2x88x921-th input data symbol. The input data symbol decision device uses the nxe2x88x921-th substitute symbol that has been estimated for determining the n-th input data symbol.
In accordance with an added feature of the invention, the substitute symbol estimation device is constructed for estimating the nxe2x88x921-th substitute symbol using the equation xc3xa2nxe2x88x921=xc3xa2nxe2x88x922 exp{jxcfx80xcex7{circumflex over (d)}nxe2x88x921}, where xc3xa2nxe2x88x921 is an estimate of the nxe2x88x921-th substitute symbol, xc3xa2nxe2x88x922 is an estimate of an nxe2x88x922-th substitute symbol; {circumflex over (d)}nxe2x88x921 is the nxe2x88x921-th input data symbol that has been determined; and xcex7 denotes a modulation index.
In accordance with an additional feature of the invention, the input data symbol decision device is constructed for determining the n-th input data symbol dn based on a phase angle of a currently obtained n-th complex-value sample symbol yn relative to a phase angle of the nxe2x88x921-th substitute symbol xc3xa2nxe2x88x921 that has been estimated for an nxe2x88x921-th time step.
In accordance with another feature of the invention, the input data symbol estimation device is an equalizer, and in an even more preferred embodiment, is a Viterbi equalizer.
According to the invention, the demodulation (that is to say the determination of the n-th input data symbol on which the CPFSK modulation is based) is based on estimating the nxe2x88x921-th substitute symbol that occurs in the linear approximation of the CPFSK. The demodulation is thus always carried out on the basis of substitute symbols that are estimated in the receiver. This means that there is no need for a fixed modulation alphabet that is already known in the receiver, and instead of this, the receiver xe2x80x9cfollowsxe2x80x9d the state of the transmitter by estimation.
In the case of demodulation without channel equalization, the n-th input data symbol dn can easily be determined on the basis of the phase angle of a currently obtained n-th complex-value sample symbol yn relative to the phase angle of the substitute symbol xc3xa2nxe2x88x921 which is estimated for the nxe2x88x921-th time step.
Alternatively, an equalizer, in particular a Viterbi equalizer, can be used to determine the n-th input data symbol dn. In this case, one advantageous measure is characterized by basing the equalization on a trellis state diagram, in which the i-th channel state relating to the time step n is described by an L-tuple:
Zni=(ZnLxe2x88x921,(i), . . . , zn1,(i), zn0,(i)), in which case the variables znLxe2x88x921,(i), . . . , zn1,(i), zn0,(i) can each assume the possible values of the input data symbols dn (L denotes the channel memory).
Other features which are considered as characteristic for the invention are set forth in the appended claims.
Although the invention is illustrated and described herein as embodied in a method and a device for demodulating CPFSK-modulated signals using a linear approximation of the CPFSK signal, it is nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the invention and within the scope and range of equivalents of the claims.
The construction and method of operation of the invention, however, together with additional objects and advantages thereof will be best understood from the following description of specific embodiments when read in connection with the accompanying drawings.